Mathematics 9709 · AS & A Level · The normal distribution

The normal distribution — practice question

For female snakes of this species, the lengths follow a normal distribution with mean $54\text{ cm}$ and standard deviation $6.1\text{ cm}$.
(a)[4]

Find the probability that a randomly selected female snake of this species has a length between $50\text{ cm}$ and $60\text{ cm}$.

(b)[5]

The lengths of male snakes of this species are also normally distributed. A scientist records the lengths of a random sample of $200$ male snakes of this species. He finds that $32$ have lengths less than $45\text{ cm}$ and $17$ have lengths more than $56\text{ cm}$. Find estimates for the mean and standard deviation of the lengths of male snakes of this species.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate standardisation: $P(\frac{50-54}{6.1}<Z<\frac{60-54}{6.1})$

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